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annotate scripts/ode/private/hermite_quartic_interpolation.m @ 20580:25623ef2ff4f

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doc: Rewrite docstrings for ode* family of functions. * scripts/ode/module.mk: Remove extra newline. * ode45.m, odeget.m, odeset.m: Rewrite docstrings. * AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m, integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m, ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m, runge_kutta_45_dorpri.m, starting_stepsize.m: Don't break @deftypefn lines. Wrap lines at 80 columns rather than 72.
author Rik <rik@octave.org>
date Sat, 03 Oct 2015 21:03:16 -0700
parents 6256f6e366ac
children eb9e2d187ed2
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1 ## Copyright (C) 2015 Jacopo Corno <jacopo.corno@gmail.com>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{x_out}] =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out})
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21 ##
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22 ## This function file can be called by an ODE solver function in order to
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23 ## interpolate the solution at the time @var{t_out} using 4th order
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24 ## Hermite interpolation.
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25 ##
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26 ## This function must be called with one output arguments: @var{x_out}
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27 ## which contains the evaluation at @var{t_out} of the Hermite interpolant.
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28 ##
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29 ## The first input argument is the vector with two given times.
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30 ##
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31 ## The second input argument is the vector with the values of the function
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32 ## to interpolate at the times specified in @var{t} and at the middle point.
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33 ##
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34 ## The third input argument is the value of the derivatives of the function
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35 ## evaluated at the two extreme points.
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36 ##
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37 ## @end deftypefn
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38 ##
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39 ## @seealso{linear_interpolation, quadratic_interpolation,
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40 ## hermite_cubic_interpolation, hermite_quintic_interpolation,
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41 ## dorpri_interpolation}
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42
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43 function x_out = hermite_quartic_interpolation (t, x, der, t_out)
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44
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45 # Rescale time on [0,1]
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46 s = (t_out - t(1)) / (t(2) - t(1));
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47
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48 # Hermite basis functions
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49 # H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4;
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50 # H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4;
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51 # H2 = 16*s.^2 - 32*s.^3 + 16*s.^4;
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52 # H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4;
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53 # H4 = s.^2 - 3*s.^3 + 2*s.^4;
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54
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55 x_out = zeros (size (x, 1), length (t_out));
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56 for ii = 1:size (x, 1)
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57 x_out(ii,:) = (1 - 11*s.^2 + 18*s.^3 - 8*s.^4)*x(ii,1) ...
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58 + ( s - 4*s.^2 + 5*s.^3 - 2*s.^4)*(t(2)-t(1))*der(ii,1) ...
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59 + ( 16*s.^2 - 32*s.^3 + 16*s.^4)*x(ii,2) ...
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60 + ( - 5*s.^2 + 14*s.^3 - 8*s.^4)*x(ii,3) ...
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61 + ( s.^2 - 3*s.^3 + 2*s.^4)*(t(2)-t(1))*der(ii,2);
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62 endfor
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63
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64 endfunction
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65
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66 ## Local Variables: ***
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67 ## mode: octave ***
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68 ## End: ***